# Category Archives: Physics

## Signatures of strongly coupled extensions of the Standard Model

The so-called lattice approach   is a very successful first principle method that allows to  solve Gauge Theories. Calculations resort to large scale simulations and are typically run on the largest supercomputers.  Lattice simulations are a unique tool to explore non perturbative phenomena in theories which are not well understood. In Nature, non perturbative phenomena

## A density of states approach to the overlap problem

Monte-Carlo methods are widely used in theoretical physics, statistical mechanics and condensed matter. Most of the applications have relied on importance sampling, which allows us to evaluate stochastically with a controllable error multi-dimensional integrals of localised functions. In lattice gauge theories, most quantities of interest can be expressed in the path integral formalism as ensemble

## Divergent Series

This project is for a student who finds the following result shocking but intriguing: 1 + 2 + 3 + . . . = -1/12 This looks wrong in so many ways what with the sum of positive terms being negative and an infinite sum being finite. The aim of the project is to understand

## Scaling

Scaling is an interesting and powerful approach to mathematics. There are many introductory applications ranging from predicting how the period of a pendulum depends on its length to why almost all animals, large and small, can jump about the same height. More sophisticated topics include fractional scaling laws in physics and biology and fractal dimensions.

## Classical Mechanics as a Field Theory

In 2013, a team of university physicists, speaking on behalf of the German Physical Society, criticised the adoption of the Karlsruhe Physics Course (KPK) at some grammar schools in South West Germany. The incriminated course suggests (among other things) to abandon the Newtonian mechanics of point particles in favour of a continuous formulation employing fields,

## Charge Dynamics in Electromagnetic Fields

In strong electromagnetic fields the Lorentz force experienced by charges can become so large that the charge motion becomes relativistic. Newton’s equation of motion, F = ma, thus has to be modified as to include relativistic effects. In other words, one has to use relativistic mechanics in order to solve for the charge dynamics. In

## Hybrid mesons from a potential model

The elementary particle called quarks combine together to form mesons. For heavy quarks the masses of the mesons can be obtained by numerically solving Schrodinger’s equation (from quantum mechanics) with a suitable potential (see http://de.arxiv.org/abs/0805.2704 for example). The potential can be modified to predict the masses of hybrid mesons. The aim of the project is

## Avalanches

An avalanche is an example of a system displaying “self-organisation”. On a clear day, the great mass of snow on a mountain may appear to be in equilibrium, but the slightest change such as a gentle breeze or the drop of a snowflake can trigger the release a dramatic amount of energy as the system

## Fireflies

Fireflies provide an example from nature of the phenomenon of synchronisation. When one firefly flashes near another, it can cause another to match the frequency of its flashing. Using analytical and/or numerical methods, the project will investigate models for synchronising oscillators, covering topics such as phase-locking and entrainment.   Supervisor: Dr Ben King

## Shock waves: Burgers’ Equation

Shock waves occur throughout nature: in fluids, gases and plasmas. A classic example is the “sonic boom” produced around an aircraft when it exceeds the speed of sound. This project will involve the study of Burgers’ equation, which is a fundamental partial differential equation that demonstrates shock wave behaviour. Using analytical and/or numerical methods, the

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